some vertices don't follow bone chain with Spline IK
I found the problem, thanks to this answer. It turns out the vertices in question were also controlled by a bone at the very end of the chain.

What I did:


select the mesh, go into edit mode;
select one vertex inside the problematic part of the mesh and bring up the properties bar by pressing N;
under Vertex Weights, check the names of the bones controlling this vertex, there should be one/several too many;
in Pose Mode, select the bone that should not be on that list;
in Weight Paint mode, choose "Subtract" as mode for the Weight Brush and paint over the red areas that should not be controlled by this bone.